In a recent SR with Oracle, the support analyst told us to disable core dumps as all the information captured in core dumps is also present in ORA-7445 trace files.
Metalink Note 397404.1 gives these two methods for disabling core dumps.
Method #1 - Set database parameter SHADOW_CORE_DUMP to NONE.
SHADOW_CORE_DUMP is a static parameter so the database must be restarted in order for the parameter value to be enabled. Setting SHADOW_CORE_DUMP to NONE will block the generation of core dumps from user (client) processes attached to the SGA. Setting this parameter has no impact on core dumps being generated by background processes. It is not possible to set BACKGROUND_CORE_DUMP to NONE. So this method will prevent core dumps from being generated by user processes but will not prevent the generation of core dumps by background processes.
Method #2 - modify the OS ULIMIT
ulimit -c 0
doing this will block core dumps from being generated by all processes executed by this user, which should include all user and background processes on the server. The database will have to be restarted in order for the new ulimit settings to take effect.